Solve 3/6^5*6^2:1/6^3

$$\frac { 3 } { 6 ^ { 5 } \cdot 6 ^ { 2 } } : \frac { 1 } { 6 ^ { 3 } }$$

Evaluate

$$\frac{1}{432}\approx 0.002314815$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$\frac{\frac{3}{6^{7}}}{\frac{1}{6^{3}}}$$

Divide \frac{3}{6^{7}} by \frac{1}{6^{3}} by multiplying \frac{3}{6^{7}} by the reciprocal of \frac{1}{6^{3}}.

$$\frac{3\times 6^{3}}{6^{7}}$$

Cancel out 6^{3} in both numerator and denominator.

$$\frac{3}{6^{4}}$$

Calculate 6 to the power of 4 and get 1296.

$$\frac{3}{1296}$$

Reduce the fraction \frac{3}{1296} to lowest terms by extracting and canceling out 3.

$$\frac{1}{432}$$

Factor

$$\frac{1}{2 ^ {4} \cdot 3 ^ {3}} = 0.0023148148148148147$$